1. Field of the Invention
The present invention relates generally to a shape simulation method, program and apparatus generating a shape of a micro device in accordance with a wafer process for fabricating semiconductors, HDD head elements, etc., and more particularly, to a shape simulation method, program and apparatus using a level set method for setting level values representing distances from a material surface to arranged lattice points to represent a surface shape.
2. Description of the Related Art
Recently, in fabrication of semiconductors, hard disk drive head elements, etc., since elements are increasingly miniaturized, a high-accuracy shape simulation is required which includes material inside information including a growth direction of a film, etc. A shape simulation apparatus for a conventional micro device has a function for outputting a final element shape formed after a manufacturing process and uses a shape change algorithm referred to as a level set method in order to calculate a shape change in the manufacturing process and the final element shape. To represent a surface shape, the level set method constructs a two-dimensional or three-dimensional virtual space for a simulation as a background, where a plurality of lattice points (nodes) is arranged, and a surface shape is represented by giving level values φ, which represent distances from a material surface, to the lattice points on the background.
FIG. 11 shows a shape representation method in the level set method in the case of a two-dimensional orthogonal lattice. An equally-spaced orthogonal lattice 100 is formed in a virtual space as a background and a material surface 102 is temporally grown in accordance with conditions of a manufacturing process in this space. Each lattice point is assigned with a level value φ representing a distance from the material surface 102 and a surface shape is represented by these level values φ. A level value assigned to a lattice point ensures a memory region corresponding to the lattice point on a memory and is stored in the memory region. With regard to a shape simulation using the level set method, a proposition has been made for increasing a speed and an accuracy of a surface shape calculation in the calculation technique of the level value.
However, in such a conventional shape simulation, since a simulation result is obtained only as level values representing a surface shape of a micro device manufactured by a semiconductor process, for example, if an element characteristic analysis such as a magnetic simulation is attempted with the use of a simulation result of a head element, because of absence of internal information of material grown by a manufacturing process, e.g., material inside information indicating a film growth direction, an estimate value must be used for necessary material inside information and, therefore, it is problematic that a analysis accuracy is deteriorated. As a method for generating such material inside information, e.g., a film growth direction through a shape simulation, it is contemplated as a method that a user separately generates and inputs a model for a growth direction or that all logs of a calculation process are recorded in a shape simulation. However, in the method of generating a growth model, it is problematic that it takes a lot of trouble and time to generate a model and, in the method of recording all logs of a calculation process, it is problematic that a huge amount of memory is used and that a calculation amount is increased since necessary inside information must be calculated separately from the obtained logs.